## 38000

38000^{2} = 1444000000 with 144 = 12^{2} and 4000000 = 2000^{2}.

by Yoshio Mimura, Kobe, Japan

## 38016

38016^{2}± 5 are primes.

38016^{2} = (2^{2} - 1)(3^{2} - 1)(5^{2} - 1)(7^{2} - 1)(10^{2} - 1)(23^{2} - 1) = (2^{2} - 1)(5^{2} - 1)(7^{2} - 1)(10^{2} - 1)(65^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 38024

38024^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 38025

38025 = 195^{2}, a square with different digits.

by Yoshio Mimura, Kobe, Japan

## 38070

38070^{2} = (20^{2} + 5)(29^{2} + 5)(65^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 38080

38080^{2} = (3^{2} - 1)(6^{2} - 1)(33^{2} - 1)(69^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 38082

38082^{2} = (1^{2} + 2)(3^{2} + 2)(8^{2} + 2)(816^{2} + 2) = (2^{2} + 2)(19^{2} + 2)(816^{2} + 2)

= (3^{2} + 2)(14^{2} + 2)(816^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 38090

38090^{2} = (1^{2} + 4)(3^{2} + 4)(17^{2} + 4)(276^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 38106

38106^{2} = (3^{2} + 9)(7^{2} + 9)(8^{2} + 9)(138^{2} + 9) = (3^{2} + 9)(65^{2} + 9)(138^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 38132

38132^{2} = 1454049424, a square pegged by 4.

by Yoshio Mimura, Kobe, Japan

## 38199

38199^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 38226

38226^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 38250

38250^{2} = (1^{2} + 9)(3^{2} + 9)(4^{2} + 9)(12^{2} + 9)(46^{2} + 9) = (1^{2} + 9)(4^{2} + 9)(6^{2} + 9)(12^{2} + 9)(29^{2} + 9)

= (1^{2} + 9)(4^{2} + 9)(21^{2} + 9)(114^{2} + 9) = (1^{2} + 9)(6^{2} + 9)(39^{2} + 9)(46^{2} + 9)

= (1^{2} + 9)(12^{2} + 9)(21^{2} + 9)(46^{2} + 9) = (3^{2} + 9)(4^{2} + 9)(5^{2} + 9)(6^{2} + 9)(46^{2} + 9)

= (3^{2} + 9)(4^{2} + 9)(39^{2} + 9)(46^{2} + 9) = (3^{2} + 9)(6^{2} + 9)(29^{2} + 9)(46^{2} + 9)

= (3^{2} + 9)(79^{2} + 9)(114^{2} + 9) = (4^{2} + 9)(6^{2} + 9)(29^{2} + 9)(39^{2} + 9)

= (4^{2} + 9)(12^{2} + 9)(21^{2} + 9)(29^{2} + 9) = (5^{2} + 9)(6^{2} + 9)(12^{2} + 9)(79^{2} + 9)

= (5^{2} + 9)(6^{2} + 9)(21^{2} + 9)(46^{2} + 9) = (12^{2} + 9)(39^{2} + 9)(79^{2} + 9)

= (21^{2} + 9)(39^{2} + 9)(46^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 38258

38258^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 38304

38304^{2} = (17^{2} - 1)(20^{2} - 1)(113^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 38313

38313^{2} = (1^{2} + 2)(3^{2} + 2)(59^{2} + 2)(113^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 38316

38316^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 38325

38325^{2} = (1^{2} + 6)(3^{2} + 6)(33^{2} + 6)(113^{2} + 6).

by Yoshio Mimura, Kobe, Japan

## 38358

38358^{2} = (2^{2} + 2)(4^{2} + 2)(3691^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 38367

38367^{2} = (16^{2} + 5)(32^{2} + 5)(74^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 38392

38392^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 38400

38400^{2} = (3^{2} - 1)(9^{2} - 1)(31^{2} - 1)(49^{2} - 1).

40^{3} + 38400 = 320^{2}, 40^{3} - 38400 = 160^{2},

200^{2} + 38400 = 280^{2}, 200^{2} - 38400 = 40^{2}.

by Yoshio Mimura, Kobe, Japan

## 38412

38412^{2} = (2^{2} + 8)(34^{2} + 8)(325^{2} + 8).

by Yoshio Mimura, Kobe, Japan

## 38416

38416 = 196^{2}4

by Yoshio Mimura, Kobe, Japan

## 38430

38430^{2} = (1^{2} + 5)(10^{2} + 5)(19^{2} + 5)(80^{2} + 5) = (4^{2} + 5)(5^{2} + 5)(19^{2} + 5)(80^{2} + 5)

= (19^{2} + 5)(25^{2} + 5)(80^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 38444

38444^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 38448

38448^{2} = (1^{2} + 8)(2^{2} + 8)(4^{2} + 8)(9^{2} + 8)(80^{2} + 8) = (1^{2} + 8)(2^{2} + 8)(8^{2} + 8)(436^{2} + 8)

= (4^{2} + 8)(8^{2} + 8)(9^{2} + 8)(98^{2} + 8) = (4^{2} + 8)(9^{2} + 8)(10^{2} + 8)(80^{2} + 8)

= (4^{2} + 8)(80^{2} + 8)(98^{2} + 8) = (8^{2} + 8)(10^{2} + 8)(436^{2} + 8).

by Yoshio Mimura, Kobe, Japan

## 38454

38454^{2} = (2^{2} + 9)(7^{2} + 9)(22^{2} + 9)(63^{2} + 9) = (5^{2} + 9)(22^{2} + 9)(297^{2} + 9)

= (7^{2} + 9)(63^{2} + 9)(80^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 38478

38478^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 38480

38480^{2}± 3 are primes.

38480^{2} = (1^{2} + 4)(2^{2} + 4)(10^{2} + 4)(12^{2} + 4)(49^{2} + 4) = (1^{2} + 4)(3^{2} + 4)(6^{2} + 4)(12^{2} + 4)(62^{2} + 4)

= (2^{2} + 4)(3^{2} + 4)(6^{2} + 4)(12^{2} + 4)(49^{2} + 4) = (2^{2} + 4)(3^{2} + 4)(16^{2} + 4)(234^{2} + 4)

= (2^{2} + 4)(4^{2} + 4)(49^{2} + 4)(62^{2} + 4) = (3^{2} + 4)(4^{2} + 4)(10^{2} + 4)(234^{2} + 4)

= (3^{2} + 4)(10^{2} + 4)(12^{2} + 4)(86^{2} + 4) = (3^{2} + 4)(12^{2} + 4)(14^{2} + 4)(62^{2} + 4)

= (6^{2} + 4)(10^{2} + 4)(12^{2} + 4)(49^{2} + 4) = (10^{2} + 4)(16^{2} + 4)(234^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 38487

38487^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 38528

38528^{2} = (1^{2} + 7)(5^{2} + 7)(6^{2} + 7)(7^{2} + 7)(49^{2} + 7) = (1^{2} + 7)(7^{2} + 7)(37^{2} + 7)(49^{2} + 7)

= (5^{2} + 7)(6^{2} + 7)(21^{2} + 7)(49^{2} + 7) = (6^{2} + 7)(7^{2} + 7)(21^{2} + 7)(37^{2} + 7)

= (21^{2} + 7)(37^{2} + 7)(49^{2} + 7).

by Yoshio Mimura, Kobe, Japan

## 38532

38532^{2} = (6^{2} + 3)(45^{2} + 3)(137^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 38544

38544^{2} = (4^{2} + 8)(6^{2} + 8)(24^{2} + 8)(49^{2} + 8).

by Yoshio Mimura, Kobe, Japan

## 38546

38546^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 38548

38548^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 38551

38551^{2} = 1059^{2} + 1060^{2} + 1061^{2} + ... + 1780^{2}.

by Yoshio Mimura, Kobe, Japan

## 38560

38560^{2} = 27^{2} + 29^{2} + 31^{2} + 33^{2} + ... + 2073^{2}.

by Yoshio Mimura, Kobe, Japan

## 38571

38571^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 38639

38639 is the fourth prime for which the Legendre symbol (a/38639) = 1 for a = 1,2,..., 28.

Page of Squares : First Upload July 7, 2012 ; Last Revised July 7, 2012by Yoshio Mimura, Kobe, Japan

## 38640

38640^{2} = (2^{2} - 1)(3^{2} - 1)(15^{2} - 1)(22^{2} - 1)(24^{2} - 1) = (5^{2} - 1)(15^{2} - 1)(22^{2} - 1)(24^{2} - 1)

= (6^{2} - 1)(47^{2} - 1)(139^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 38646

38646^{2} = (1^{2} + 2)(6^{2} + 2)(26^{2} + 2)(139^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 38655

38655^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 38656

38656^{2} = (3^{2} + 7)(5^{2} + 7)(12^{2} + 7)(139^{2} + 7).

by Yoshio Mimura, Kobe, Japan

## 38672

38672^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 38710

38710^{2} = (1^{2} + 6)(2^{2} + 6)(22^{2} + 6)(209^{2} + 6) = (8^{2} + 6)(22^{2} + 6)(209^{2} + 6).

by Yoshio Mimura, Kobe, Japan

## 38719

38719^{2} = 159^{2} + 161^{2} + 163^{2} + 165^{2} + ... + 2079^{2}.

by Yoshio Mimura, Kobe, Japan

## 38760

293^{2} + 38760 = 353^{2}, 293^{2} - 38760 = 217^{2}.

by Yoshio Mimura, Kobe, Japan

## 38772

38772^{2} = 15032679844

by Yoshio Mimura, Kobe, Japan

## 38776

38776^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 38836

38836^{2} = (2^{2} + 3)(17^{2} + 3)(859^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 38841

38841^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 38868

29802^{2} + 38868^{2} = 2398880628, a mosaic square.

by Yoshio Mimura, Kobe, Japan

## 38880

234^{2} + 38880 = 306^{2}, 234^{2} - 38880 = 126^{2}.

by Yoshio Mimura, Kobe, Japan

## 38934

38934^{2} = (1^{2} + 5)(2^{2} + 5)(11^{2} + 5)(472^{2} + 5) = (1^{2} + 5)(4^{2} + 5)(7^{2} + 5)(472^{2} + 5)

= (2^{2} + 5)(3^{2} + 5)(7^{2} + 5)(472^{2} + 5) = (7^{2} + 5)(11^{2} + 5)(472^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 38961

38961^{2} = 108^{4} + 135^{4} + 180^{4}.

by Yoshio Mimura, Kobe, Japan

## 38982

38982^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 38994

38994^{2} = (17^{2} + 2)(20^{2} + 2)(114^{2} + 2).

by Yoshio Mimura, Kobe, Japan